Universality and tree structure of high-energy QCD

Using nontrivial mathematical properties of a class of nonlinear evolution equations, we obtain the universal terms in the asymptotic expansion in rapidity of the saturation scale and of the unintegrated gluon density from the Balitskii-Kovchegov equation. These terms are independent of the initial conditions and of the details of the equation. The last subasymptotic terms are new results and complete the list of all possible universal contributions. Universality is interpreted in a general qualitative picture of high-energy scattering, in which a scattering process corresponds to a tree structure probed by a given source.